jdc2: A terrific problem! I saw a completely wrong line and missed it entirely. I saw Bf4+ 2.Kb1 (Q or R moves to block result in mate by Ra1)Ra1+ 3.Kxa1 Ra8+ 4.Kb1 Qa5 but didn't see that the white bishop could go to a4 to block, also that after Qa5 the white pawn could go to c3.

jdc2: I sometimes play one engine against another using a starting position from an actual game, in order to see other possibilities. I used the position after Black's move 9 here and for some reason the engines did this: [Date "2016.04.29"]
[White "Stockfish 240416 64 POPCNT"]
[Black ...